e) `(2\sqrt{5})/(\sqrt{3}+1)+(3\sqrt{3})/(\sqrt{5}-\sqrt{2})+(\sqrt{2})/(\sqrt{3}+\sqrt{2})-4/(\sqrt{5}-3)`
`=(2\sqrt{5}(\sqrt{3}-1))/((\sqrt{3}+1)(\sqrt{3}-1))+(3\sqrt{3}(\sqrt{5}+\sqrt{2}))/((\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2}))+(\sqrt{2}(\sqrt{3}-\sqrt{2}))/((\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2}))-(4(\sqrt{5}+3))/((\sqrt{5}-3)(\sqrt{5}+3))`
`=(2\sqrt{5}(\sqrt{3}-1))/(3-1)+(3\sqrt{3}(\sqrt{5}+\sqrt{2}))/(5-2)+(\sqrt{2}(\sqrt{3}-\sqrt{2}))/(3-2)-(4(\sqrt{5}+3))/(5-9)`
`=(2\sqrt{5}(\sqrt{3}-1))/(2)+(3\sqrt{3}(\sqrt{5}+\sqrt{2}))/(3)+(\sqrt{2}(\sqrt{3}-\sqrt{2}))/(1)-(4(\sqrt{5}+3))/(-4)`
`=\sqrt{5}(\sqrt{3}-1)+\sqrt{3}(\sqrt{5}+\sqrt{2})+\sqrt{2}(\sqrt{3}-\sqrt{2})+\sqrt{5}+3`
`=\sqrt{15}-\sqrt{5}+\sqrt{15}+\sqrt{6}+\sqrt{6}-2+\sqrt{5}+\sqrt{3}`
`=(\sqrt{15}+\sqrt{15})+(\sqrt{6}+\sqrt{6})+(\sqrt{5}-\sqrt{5})+(3-2)`
`=2\sqrt{15}+2\sqrt{6}+1`
